In English and Italian there are words and phrases such as lovesick or malato d'amore, which directly come from the analogy love as a sickness. Since this are very common expressions, I was wondering, if in German there are some similar phrases or words, which refer to the same analogy. On Duden I found liebeskrank and Liebeskummer. I am not sure about their popularity and if people actually would say something like that to describe people who are in love. Concerning Liebeskummer, I think it refers only to a sadness condition caused by love rejection and not really to an actual sickness, am I right? Are there other such expressions?
For the words you suggested:
Liebeskrank refers to being so much in love that you can't make rational decisions or as DUDEN describes it:
sich aus Verliebtheit in einem Zustand der Übererregtheit befindend
Liebeskummer refers to a depressed feeling because of (rejected) love, again DUDEN:
durch eine unglückliche Liebesbeziehung verursachte gedrückte Stimmung
Other words that I would sugest:
Herzschmerz refers to pain in the heart but is often used similarly to Liebeskummer in colloquial.
gebrochenes Herz (german for "broken heart") is sometimes used similarly to Liebeskummer, although not as a noun. Example:
Sie hat mein Herz gebrochen.
verrückt vor Liebe (german for "madly in love")
liebestoll (again german for "madly in love", adj) which has almost the same meaning as "verrückt vor Liebe".
These last two refer more to the feeling at the beginning of or before a relationship rather than afterwards.
The usage of these terms varies by location, age of author/speaker and hundreds of other parameters. Most of the given examples are only used by people with an much bigger vocabulary than what's used in most conversations.
Here is what my German teenager says.
Liebeskummer is commonly used in Germany today, even among teenagers. Often Liebeskummer is used when a couple breaks up and then you are heartbroken and cry a lot. Liebeskummer is not an actual sickness -- it is just a saying.
Liebeskrank on the other hand she never heard about and says that this must not be commonly used.
Now, if you were looking for a German translation of the American slang "bae" (or "crush") then the term is "Schwarm". So, imagine that a boy really likes a girl, but isn't dating her -- she would be his "Schwarm". This would be the closest German term to the English word "lovesick".